There is significant evidence to show that physical activity reduces the risk of many chronic diseases. With the rise of mobile health (mHealth) technologies, one promising approach is to design interventions that are responsive to an individual's changing needs. This is the overarching goal of Just Walk, an intensively adaptive physical activity intervention that has been designed on the basis of system identification and control engineering principles. Features of this intervention include the use of multisine signals as pseudo-random inputs for providing daily step goals and reward targets for participants, and an unconventional ARX estimation-validation procedure applied to judiciously-selected data segments that seeks to balance predictive ability over validation data segments with overall goodness of fit. Analysis of the estimated models provides important clues to individual participant characteristics that influence physical activity. The insights gained from black-box modeling are critical to building semi-physical models based on a dynamic extension of Social Cognitive Theory.